A novel natural image noise level estimation based on flat patches and local statistics

  • Zhuang Fang
  • Xuming YiEmail author


This paper proposes a high-precision algorithm for noise level estimation. Different from existing algorithms, we present a new noise level estimation algorithm by linearly combining the overestimated and underestimated results using combinatorial coefficients that can be tailored to the problem at hand. The algorithm has two distinct features: it avoids the underestimation of noise level estimation algorithms that employ the minimum eigenvalue and demonstrates higher accuracy and robustness for a large range of visual content and noise conditions. The experimental results that are obtained in this study demonstrate that the proposed algorithm is effective for various scenes with various noise levels. The software release of the proposed algorithm is available online at


Noise level estimation Flat patches Gaussian noise Eigenvalue Covariance matrix 



This study was supported by the National Natural Science Foundation of China (Grant no. 11671307, 61561019, 61763009 and 11761030), the Nature Science Foundation of Hubei Province (Grant no. 2015CFB262), and the Doctoral Scientific Fund Project of Hubei University for Nationalities (Grant no. MY2015B001). We would like to express our gratitude to the anonymous reviewers and editors for their valuable comments and suggestions, which led to the improvement of the original manuscript.


  1. 1.
    Abdallah MB, Azar AT, Guedri H, Malek J, Belmabrouk H (2018) Noise-estimation-based anisotropic diffusion approach for retinal blood vessel segmentation. Neural Comput Appl 29(8):159–180CrossRefGoogle Scholar
  2. 2.
    Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54 (11):4311–4322CrossRefGoogle Scholar
  3. 3.
    Arbeláez P, Maire M, Fowlkes C, Malik J (2011) Contour detection and hierarchical image segmentation. IEEE Trans Pattern Anal Mach Intell 33(5):898–916CrossRefGoogle Scholar
  4. 4.
    Callet PL, Autrusseau F (2005) Subjective quality assessment irccyn/ivc database.
  5. 5.
    Chen G, Zhu F, Heng PA (2015) An efficient statistical method for image noise level estimation. In: 2015 I.E. international conference on computer vision (ICCV), pp 477–485Google Scholar
  6. 6.
    Colom M, Lebrun M, Buades A, Morel JM (2015) A non-parametric approach for the estimation of intensity-frequency dependent noise. In: 2015 IEEE international conference on image processing, pp 4261–4265Google Scholar
  7. 7.
    Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Trans Image Process 18 (8):2080–2095CrossRefGoogle Scholar
  8. 8.
    Dong W, Zhang L, Shi G, Wu X (2011) Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans Image Process 20(7):1838–1857MathSciNetCrossRefGoogle Scholar
  9. 9.
    Dong W, Zhang L, Shi G, Li X (2013) Nonlocally centralized sparse representation for image restoration. IEEE Trans Image Process 22(4):1620–1630MathSciNetCrossRefGoogle Scholar
  10. 10.
    Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41 (3):613–627MathSciNetCrossRefGoogle Scholar
  11. 11.
    Donoho DL, Johnstone IM (1995) Adapting to unknown smoothness via wavelet shrinkage. Publ Am Stat Assoc 90(432):1200–1224MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ghazi MM, Erdogan H (2016) Image noise level estimation based on higher-order statistics. Multimed Tools Appl 76(2):1–19Google Scholar
  13. 13.
    Hashemi M, Beheshti S (2010) Adaptive Noise Variance Estimation in BayesShrink. IEEE Signal Process Lett 17(1):12–15CrossRefGoogle Scholar
  14. 14.
    Huang X, Chen L, Tian J, Zhang X, Fu X (2014) Blind noisy image quality assessment using block homogeneity. Comput Electr Eng 40(3):796–807CrossRefGoogle Scholar
  15. 15.
    Jiang P, Zhang JZ (2016) Fast and reliable noise level estimation based on local statistic. Pattern Recogn Lett 78(C):8–13MathSciNetCrossRefGoogle Scholar
  16. 16.
    Khmag A, Ramli AR, Al-Haddad SAR, Kamarudin N (2018) Natural image noise level estimation based on local statistics for blind noise reduction. Vis Comput 34(4):575–587CrossRefGoogle Scholar
  17. 17.
    Kim DG, Shamsi ZH (2018) Enhanced residual noise estimation of low rank approximation for image denoising. Neurocomputing 293:1–11CrossRefGoogle Scholar
  18. 18.
    Li D, Zhou J, Tang YY (2017) Noise Level Estimation for Natural Images Based on Scale-Invariant Kurtosis and Piecewise Stationarity. IEEE Trans Image Process 26 (2):1017–1030MathSciNetCrossRefGoogle Scholar
  19. 19.
    Liu X, Tanaka M, Okutomi M (2013) Single-image noise level estimation for blind denoising. IEEE Trans Image Process 2(12):5226–5237CrossRefGoogle Scholar
  20. 20.
    Mandal S, Bhavsar A, Sao AK (2016) Noise adaptive super-resolution from single image via non-local mean and sparse representation. Signal Process 132:134–149CrossRefGoogle Scholar
  21. 21.
    Olsen SI (1993) Estimation of noise in images: an evaluation. Cvgip Graph Model Image Process 55(4):319–323CrossRefGoogle Scholar
  22. 22.
    Oyet AJ, Sutradhar B (2003) Testing variances in wavelet regression models. Stat Probab Lett 61(1):97–109MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ponomarenko P, Lukin V, Zelensky A, Egiazarian K, Carli M, Battisti F (2009) Tid2008-a database for evaluation of full-reference visual quality assessment metrics. Adv Modern Radioelectron 10(4):30–45Google Scholar
  24. 24.
    Pyatykh S, Hesser J, Zheng L (2013) Image noise level estimation by principal component analysis. IEEE Trans Image Process 22(2):687–699MathSciNetCrossRefGoogle Scholar
  25. 25.
    Royston JP (1982) Algorithm as 177: Expected normal order statistics (exact and approximate). J R Stat Soc 31(2):161–165Google Scholar
  26. 26.
    Shapiro SS, Wilk MB (1972) An analysis of variance test for the exponential distribution (complete samples). Technometrics 14(2):355–370CrossRefGoogle Scholar
  27. 27.
    Sheikh HR, Sabir MF, Bovik AC (2005) Live image quality assessment database release2. Accessed 3 May 2017
  28. 28.
    Shi B, Pang ZF, Wu J (2015) Alternating split Bregman method for the bilaterally constrained image deblurring problem. Appl Math Comput 250:402–414MathSciNetzbMATHGoogle Scholar
  29. 29.
    Shin DH, Park RH, Yang S, Jung JH (2005) Block-based noise estimation using adaptive Gaussian filtering. IEEE Trans Consum Electron 51(1):218–226CrossRefGoogle Scholar
  30. 30.
    Witwit W, Zhao Y, Jenkins K, Addepalli S (2018) Global motion based video super-resolution reconstruction using discrete wavelet transform. Multimedia Tools Appl 77(20):27641–27660CrossRefGoogle Scholar
  31. 31.
    Xie X, Wang C, Zhang A, Meng X (2014) A robust level set method based on local statistical information for noisy image segmentation. Optik 125(9):2199–2204CrossRefGoogle Scholar
  32. 32.
    Xu S, Yang X, Jiang S (2017) A fast nonlocally centralized sparse representation algorithm for image denoising. Signal Process 131:99–112CrossRefGoogle Scholar
  33. 33.
    Zhu X, Milanfar P (2010) Automatic parameter selection for denoising algorithms using a no-reference measure of image content. IEEE Trans Image Process 19(12):3116–3132MathSciNetCrossRefGoogle Scholar
  34. 34.
    Zoran D, Weiss Y (2009) Scale invariance and noise in natural images. In: 2009 I.E. international conference on computer vision (ICCV), pp 2209–2216Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhan,People’s Republic of China
  2. 2.School of ScienceHubei University for NationalitiesEnshiPeople’s Republic of China

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